Analysis for two-dimensional inverse quasilinear parabolic problem by Fourier method

References

• Ramm AG. Inverse problems-mathematical and analytical techniques with application to engineering. New York: Springer; 2005.
   Google Scholar
• Sharma PR, Methi G. Solution of two dimensional parabolic equation subject to non-local conditions using homotopy perturbation method. J Appl Commun Sci. 2012;1:12–16.
   Google Scholar
• Ivanchov M, Vlasovi V. Inverse problem for a two-dimensional strongly degenerate heat equation. Electron J Differ Equ. 2018;77:1–17.
   Google Scholar
• Dehghan M. A new AD1 technique for two-dimensional parabolic equation with an integral condition. Pergamon Comput Math Appl. 2002;43:1477–1488.
   Google Scholar
• Dehghan M. A finite difference method for a non-local boundary value problem for two dimensional heat equation. Appl Math Comput. 2000;112:133–142.
   Google Scholar
• Afshar S, Soltanalizadeh B. Solution of the two dimensional second-order diffusion equation with nonlocal boundary condition. Int J Pure Appl Math. 2014;94(2):119–131.
   Google Scholar
• Gumel B, Ang WT, Twizellc EH. Efficient parallel algorithm for the two-dimensional diffusion equation subject to specification of massa. Int J Comput Math. 1997;64(1–2):153–163.
   Google Scholar
• Samaneh A, Soltanalizadeh B. Solution of the two-dimensional second-order diffusion equation with nonlocal boundary conditions. Int J Pure Appl Math. 2014;94(2):119–131.
   Google Scholar
• Dehghan M, Implicit solution of a two-dimensional parabolic inverse problem with temperature overspecification. J Comput Anal Appl. 2001;3(4):35–43.
   Google Scholar
• Kumar BVR, Priyadarshi G. Haar wavelet method for two-dimensional parabolic inverse problem with a control parameter. Rend Circ Mat Paler Ser 2. 2020;69:961–976.
   Google Scholar
• Mohebbi A. A numerical algorithm for determination of a control parameter in two-dimensional parabolic inverse problems. Acta Math Appl Sin. 2011;31(1):213–224. English Series.
   Google Scholar
• Li F, Wua Z, Ye C. A finite difference solution to a two-dimensional parabolic inverse problem. Appl Math Model. 2012;36:2303–2313.
   Google Scholar
• Dehghan M. Finite difference schemes for two-dimensional parabolic inverse problem with temperature overspecification. Int J Comput Math. 2000;75:339–349.
   Google Scholar
• Dehghan M. Identifying a control function in two dimensional parabolic inverse problems. Appl Math Comput. 2003;143(2):375–391.
   Google Scholar
• Meng Z, Zhao Z. Hermite spectral method for solving inverse heat source problems in multiple dimensions. Inverse Probl Sci Eng. 2017;25(9):1243–1258.
   Google Scholar
• Hill GW. On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon. Acta Math. 1886;8:1–36.
   Google Scholar
• Baglan I, Kanca F. An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition. Math Methods Appl Sci. 2015;38(530):851–867.
   Google Scholar
• Baglan I. Determination of a coefficient in a quasilinear parabolic equation with periodic boundary condition. Inverse Probl Sci Eng. 2015;23(5):884–900.
   Google Scholar
• Baglan I, Kanca F. Two-dimensional inverse quasilinear parabolic problem with periodic boundary condition. Appl Anal. 2019;98(8):1549–1565.
   Google Scholar
• Kanca F, Baglan I. Solution of the boundary-value problem of heat conduction with periodic boundary conditions. Ukr Math J. 2020;72(2):110–125.
   Google Scholar
• Ionkin NI, Solution of a boundary-value problem in heat conduction with a nonclassical boundary condition. Differ Equ. 1977;13:204–211.
   Google Scholar
• Feng P, Karimov ET. Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations. J Inverse Ill-Posed Probl. 2015;23(4):339–353.
   Google Scholar
• Atangana A, Mekkaoui T. Trinition the complex number with two imaginary parts: fractal fractal, chaos and fractional calculus. Chaos Solitons Fractals. 2019;128:366–381.
   Google Scholar
• Atangana A, Araz SI. Analysis of a new partial integro-differential equation with mixed fractional operators. Chaos Solitons Fractals. 2019;127:257–271.
   Google Scholar
• Atangana A, Sha A. Differential and integral operators with constant fractional order and variable fractional dimension. Chaos Solitons Fractals. 2019;127:226–243.
   Google Scholar